# Topology optimization of freeform large-area metasurfaces

## TL;DR

This paper presents a scalable topology optimization method for large-area, multi-frequency metasurfaces, enabling the discovery of complex designs with unprecedented degrees of freedom and multi-layer configurations.

## Contribution

It extends topology optimization to large metasurface areas using a locally periodic approximation, allowing for the design of both sub- and supra-wavelength patterns across multiple frequencies and angles.

## Key findings

- Successfully optimized metasurfaces with over 10^6 degrees of freedom.
- Discovered novel multi-layer, multi-frequency metasurface designs.
- Achieved designs that control both near and far fields.

## Abstract

We demonstrate optimization of optical metasurfaces over $10^5$--$10^6$ degrees of freedom in two and three dimensions, 100--1000+ wavelengths ($\lambda$) in diameter, with 100+ parameters per $\lambda^2$. In particular, we show how topology optimization, with one degree of freedom per high-resolution "pixel," can be extended to large areas with the help of a locally periodic approximation that was previously only used for a few parameters per $\lambda^2$. In this way, we can computationally discover completely unexpected metasurface designs for challenging multi-frequency, multi-angle problems, including designs for fully coupled multi-layer structures with arbitrary per-layer patterns. Unlike typical metasurface designs based on subwavelength unit cells, our approach can discover both sub- and supra-wavelength patterns and can obtain both the near and far fields.